Triple Pentominoes Update

Livio Zucca's Triple Pentominoes studies the problem of finding a minimal figure that can be tiled with any of three pentominoes. Many of the solutions are complex. Where no planar solution is known, a reëntrant solution is given. Solutions were contributed by Paolo Licheri, Mauro Casini, Gabriele Carelli, Odette De Meulemeester, Andrew Clarke, Giovanni Resta, Silvio Sergio, Patrick Hamlyn, Jorge Luis Mireles, Mauro Carelli, Mauro De Filippis, and Zucca.

At least four of the solutions can be improved, and at least one of the unsolved cases has a reëntrant solution.

Here is a solution for I+N+W with 10 tiles, replacing one with 20:

Here is a solution for I+P+V with 10 tiles, replacing one with 30:

Here is a solution for I+W+Y with 12 tiles, replacing one with 20:

Here is a solution for P+U+Y with 16 tiles, replacing one with 24:

And here is a reëntrant solution for F+U+Z:

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Col. G. L. Sicherman [ HOME | MAIL ]